The Gunners had a £90m bid for the France winger accepted in the summer.
They wanted him on board as Alexis Sanchez’s replacement after agreeing to sell the Chilean to Manchester City for £60m.
Neither deal went through though, and now Liverpool are chasing down Lemar.
Journalist Duncan Castles claims the Monaco man has already been convinced into a move by Jurgen Klopp.
And he thinks that spells trouble for Arsenal.
Castles said on The Transfer Window podcast: "It's possible Arsenal will try and bid again but it will be very difficult and embarrassing for them to do.
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“It's possible Arsenal will try and bid again but it will be very difficult and embarrassing for them to do”
Duncan Castles
"It's possible in the sense they take money from selling Alexis Sanchez and they will need a player in.
"They may go back to what they were going to do in the summer when their solution was to take that money and add some more to it and buy Lemar on the last day of the window.
"Having already rejected them once and the player having told Liverpol his preference to go there over them, they are likely to be embarrassed again in that pursuit.
“It doesn't mean they won't try but it wouldn't be particularly sensible to try.”